The suggestion about the auto shutoff sounds like the best I've heard. There's a tiny pipe that gets heated by the flame. It's a thermocouple (produces electricity from the heat) and that tells the controller that the flame is ON. If thats damaged, no juice. After the programmed time, the controller sees no current there and shuts off the gas to prevent a buildup of unfired gasses, preventing the loud and disconcerting boom and uncontrolled fire. This must be fixed or (more likely today) replaced (probably the entire controller) by a qualified tech.
The other possibility that occurs to me is a lack of sufficient gas flow to the burner, possibly caused by a kinked or squashed propane
line somewhere between the tank and the burner. This would allow sufficient pressure to light
the burner, but as the main flame consumed the gas in the line, the pressure and flow would drop, causing the shutoff. Gas is still flowing slowly, the pressure would rebuild allowing a relight and repeat.
Either scenario is possible, but you can check the gas line visually without spending money on a technician. If that doesn't look like the problem, take it to a pro.
And check to make sure your camper's propane
alarm is working, so you won't be asphyxiated or blown up in the night by a propane
leak. Propane is heavier than air, so tends to pool up (as would water) in anyplace where it can't flow out.